The value of 12 C 2-13 C 3-14 C 4-999 C 989 isA- 1000 C11-12B- 1000 C11-12- 999 C11-12D- 1000 C989

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The value of $^{12} C_{2} +^{13} C_{3} +^{14} C_{4} + . . . . . . . . +^{999} C_{989}$ is

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^{12} C_{2} +^{13} C_{3} +^{14} C_{4} + . . . +^{999} C_{989}

^{1000} C_{a} + b

| a + b | =

a + b)

^{12} C_{2} +^{13} C_{3} +^{14} C_{4} + . . . +^{999} C_{989}

^{1000} C_{a} + b

| a + b | =

a + b)

\frac{1}{2}

- \frac{1}{2}

- \frac{1}{8}

100 lim n \to 200 [C_{1} - (1 + \frac{1}{2}) C_{2} + (1 + \frac{1}{2} + \frac{1}{3}) C_{3} - \dots + (- 1)^{n - 1} (1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}) C_{n}]

C_{r} =^{n} C_{r}

\lim_{x \to 0} \frac{\cos e c x - \cot x}{x} is

- \frac{1}{2}

\frac{1}{2}

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